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wu :: forums    riddles    putnam exam (pure math) (Moderators: william wu, towr, Grimbal, Icarus, Eigenray, SMQ)    Limit of a Combinatorial Sum « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Limit of a Combinatorial Sum  (Read 789 times) Michael Dagg Senior Riddler     Gender: Posts: 500 Limit of a Combinatorial Sum   « on: Aug 1st, 2008, 11:51am » Quote Modify Suppose     G(m) = \sum_{i=1}^m  \sum_{j=1}^m C(m,i) C(m,j) i^{m-j} j^{m-i}  .   Show that   lim m->oo [ (G(m))^{1/(2m)}  ln m ]/m = 1/e   . « Last Edit: Aug 3rd, 2008, 8:47am by Michael Dagg » IP Logged Regards, Michael Dagg Obob Senior Riddler     Gender: Posts: 489 Re: Limit of a Combinatorial Sum   « Reply #1 on: Aug 1st, 2008, 1:54pm » Quote Modify Should that be j^{m-1} or j^{m-i}? IP Logged Michael Dagg Senior Riddler     Gender: Posts: 500 Re: Limit of a Combinatorial Sum   « Reply #2 on: Aug 2nd, 2008, 8:38pm » Quote Modify Sorry, I made typo --   j^{m-i}   is correct.  Good observation, however, I hope   no one spent any time on it -- as written, the sum (whose terms are all positive)   exceeds the term when   i=j=m   and that term is   m^{m-1}  . IP Logged Regards, Michael Dagg Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs => putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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